MCV4U - Lesson Plan - GZhang

Teacher: Gale Zhang Lesson Plan Breakdown St. Harvard College

LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Rate of Change – Secant and Tangent

DATE(S): Day 1 PERIOD/TIME(S): 3 hours

CURRICULUM EXPECTATIONS: By the end of this lesson, students will

- demonstrate an understanding of the concept of rate of change- demonstrate an understanding of the slope of the secant and tangent- demonstrate the ability to applications involving rate of change by using the average slope, secant, and

the instantaneous slope tangent- demonstrate the ability to evaluate algebraic expressions involving secant and tangent

ASSESSMENT/EVALUATION STRATEGIES:The assessment strategies for this lesson will include:

- students’ participation level in class during Socratic instructions- students’ response time during a question and answer section with the teacher- students’ performance level during assigned in class work

The evaluation strategies for this lesson will include:- students’ performance is not evaluated at Day 1

ACCOMODATIONS:

TEACHING STRATEGIES: SUMMARY OF LESSON PLAN

Socratic Lessons: The academic content will be taught through board works

Introduction- Introduction to the course outline- Introducing, reviewing the concept of rate of change as well as secant and tangent

Small-Group Discussion: students will discuss various concepts in this lesson among peers

Middle- Understanding the new concepts and apply them to the problems during the work period section

Conclusion- Students should be able to solve applications and algebraic expressions related to secant and tangents

RESOURCES:Textbook, Print publications

Follow-up/Homework/Extensions/RemindersAdditional Exercise handout


LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Rate of Change and Limits



- demonstrate an understanding of the concept limits- demonstrate an understanding of the relationship between tangent and limit- demonstrate the understanding of left side limit and right side limit- demonstrate the ability to evaluate simple limit expressions- demonstrate the ability to determine whether an limit exist




ACCOMODATIONS:



Introduction- Introduction to the concept of limit- Demonstration of techniques for evaluating simple limits (properties of limits)



Conclusion- Students should be able to solve various limits by algebraic methods



LESSON PLAN


COURSE: MCV4U UNIT/TOPIC: Indeterminate Limits



- demonstrate an understanding of the concept of indeterminate limits- demonstrate the ability to identify the various forms of indeterminate limits- demonstrate the ability to evaluate algebraically various forms of indeterminate limits



The evaluation strategies for this lesson will include:- 15 ~ 20 minutes quiz

ACCOMODATIONS:



Introduction- Introducing various techniques for solving indeterminate limits



Conclusion- Students should be able to solve various indeterminate limits algebraically



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Limit by Change of Variable




- demonstrate an understanding of the limitations of the current techniques- demonstrate an understanding of the concept of change of variable- demonstrate the ability to use change of variable technique to solve advanced limits




ACCOMODATIONS:



Introduction- Introducing various techniques to apply the change of variable method to limits



Conclusion- Students should be able to solve advanced limits by using the change of variable method



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Limits of Absolute Values




- demonstrate an understanding of the concept of absolute values and how it affects limits- demonstrate the ability to convert limits with absolute value bars to left side limit and right side limits- demonstrate the ability to evaluate limits with absolute value bars including the ones that DNE




ACCOMODATIONS:



Introduction- Demonstrating techniques and critical criteria involving evaluation of absolute limits



Conclusion- Students should be able to solve limits including absolute value bars



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Limits of Infinities




- demonstrate an understanding of the concept of end behaviour and how it relates to the limits at infinity- demonstrate the ability to evaluate limits at infinities




ACCOMODATIONS:



Introduction- Reviewing the sketching rules for rational function in MHF4U and make relations to the limits of infinities



Conclusion- Students should be able to evaluate algebraically the limits at infinities



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Limits that Crashes




- demonstrate an understanding of the concept of one-side-only limits- demonstrate an understanding of the reason why some limit only exist on one side- demonstrate the ability to recognize when a limit becomes DNE, yet one side is infinites- demonstrate the ability to evaluate limit that crashes by using one-sided limits



The evaluation strategies for this lesson will include:- 10 ~ 15 minutes quiz

ACCOMODATIONS:



Introduction- Showing various techniques in factoring out the ‘bad guy’



Conclusion- Students should be able to evaluate limits that crashes the function, and identity the infinities one side is belonging to



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Review of Unit 1 and Unit Test



CURRICULUM EXPECTATIONS: Evaluation and review day, no new curriculum expectation is taught.


- students’ response time during a question and answer section with the teacher- students’ performance level during the review lecture section- students’ performance level during the review assignment section

The evaluation strategies for this lesson will include:- Summative evaluation for Unit 1 – Limits and Derivatives

ACCOMODATIONS: English Language Learners: Students who have difficulty with English is allowed to use the dictionary (paper or electronic). ELLs may ask the teacher for help to clarify questions, though depending on the nature of the question, the teacher might not be answering it if according to his/her judgment that question exceeds the help for a pure language issue.



Introduction- Review of contents taught in Unit 1


Middle- Students will be working on a review assignment- Help those students who are having difficulties

Assignment: Students will be working on an assignment as a review exercise for the test

Conclusion- Summative Evaluation for the first unit

RESOURCES:Various Textbooks

Follow-up/Homework/Extensions/Reminders

LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Differentiation Rules




- demonstrate an understanding of the power rule, product rule, and quotient rule- demonstrate the ability to apply various differentiation rules to algebraic problems




ACCOMODATIONS:



Introduction- Demonstrating various ways to apply the differentiation techniques to algebraic expressions



Conclusion- Students should be able to apply the differentiation rules to algebraic expressions



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Geometric Applications




- demonstrate an understanding of the concept of geometric key terms, i.e., parallel, perpendicular- demonstrate the ability to apply the mastered differentiation techniques to geometric problems- demonstrate the ability to find the slope of tangent to a function under various conditions




ACCOMODATIONS:



Introduction- Introducing basic concepts in the geometric problems and make connections to the differentiation rules mastered last period



Conclusion- Students should be able to solve various geometric problems with differentiation



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Chain Rule and Implicit Differentiation




- demonstrate an understanding of the chain rule and apply it to differentiation complicate functions- demonstrate an understanding of implicit differentiation and its benefits- demonstrate the ability to differentiate complicated composite function by using the chain rule- demonstrate the ability to differentiate complicated implicit functions




ACCOMODATIONS:



Introduction- Introducing the chain rule as a techniques to differentiate complicated composite functions



Conclusion- Differentiate composite functions and implicit function by applying the chain rule



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Increasing and Decreasing Functions




- demonstrate an understanding of the rate of change as how it relates to the increasing and decreasing aspects of functions

- demonstrate an understanding of the concept of increasing/decreasing functions and its relevant significance to the application

- demonstrate the ability to find the intervals in which a function is increasing or decreasing




ACCOMODATIONS:



Introduction- Introducing the first derivative test method to identify intervals of increasing/decreasing functions



Conclusion- Find intervals of increase or decrease for a particular function and understand its importance when applied to a real life application



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Rate of Change and Local Extrema




- demonstrate an understanding of the concept of local extrema- demonstrate an understanding of absolute max/min, and global max/min- demonstrate the ability to repeat the procedure in finding local max/min, and absolute max/min




ACCOMODATIONS:



Introduction- Demonstrate the procedures for finding local, global, and absolute maximum and minimum



Conclusion- Able to find, distinguish, and apply for local, global, and absolute max/min, to algebraic expressions as well as applications



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Optimization Applications




- demonstrate an understanding of the concept of optimization applications- demonstrate the ability to evaluate and find the optimized value- demonstrate the ability to translate the algebraic expertise into interpretations to the related applications




ACCOMODATIONS:



Introduction- Introducing techniques and procedures for finding the optimized value



Conclusion- Find optimized value for a real life application and translated the algebraic solution into a meaningful statement regarding the result



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Related Rates




- demonstrate an understanding of the concept of related rates- demonstrate the ability to solve related rates algebraically- demonstrate the ability to translate the algebraic solution to a meaningful interpretation




ACCOMODATIONS:



Introduction- Demonstrate the exact procedure for finding the algebraic solution for related rates applications



Conclusion- Solve related rates application algebraically and provide a meaningful interpretation









The evaluation strategies for this lesson will include:- Summative evaluation for Unit 2 –Derivatives and Its Applications








Conclusion- Summative Evaluation for the second unit



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Derivatives of Exponential Functions




- demonstrate an understanding differentiation rules with exponential functions- demonstrate the ability to differentiate exponential expressions with chain rule, etc- demonstrate the ability to differentiate exponential expressions implicitly




ACCOMODATIONS:



Introduction- Procedures and techniques involved in evaluating the derivatives of exponential expressions



Conclusion- Find derivatives of exponential functions and apply it in solving problems related to the slope of tangent, and geometric applications



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Rate of Change for Growth and Decay




- demonstrate an understanding of the concept for applying the derivatives to applications- demonstrate the ability to model an application with growth and decay using an exponential model- demonstrate the ability to solve applications using derivatives



The evaluation strategies for this lesson will include:- 10 ~ 15 minutes mini quiz on differentiation rules

ACCOMODATIONS:



Introduction- Procedures for modelling rate of change in application, and applying the derivative to solve various growth and decay problems



Conclusion- Solve applications involving growth and decay by applying the concept of derivatives for exponential functions



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Logarithmic Derivatives and Optimization




- demonstrate the ability to differentiate expressions with logarithms including chain rules and implicit differentiations

- demonstrate the ability to model an application with growth and decay using a logarithmic model- demonstrate the ability to solve applications using derivatives




ACCOMODATIONS:



Introduction- Procedures for deriving the differentiation rule for logarithmic expressions- Techniques for solving optimization applications involving exponential and logarithmic expressions



Conclusion- Solve optimization applications by applying the derivative function



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Properties of Sketching and Asymptotes




- demonstrate an understanding of the concept of various asymptotes- demonstrate an understanding of the procedures for general curve sketching- demonstrate the ability to identify x-int, y-int, horizontal, vertical, and oblique asymptotes- demonstrate the ability to identify increasing/decreasing intervals for a function- demonstrate the ability to identify local extrema (maximum/minimum) for a function




ACCOMODATIONS:



Introduction- Demonstrate the procedures for sketching a polynomial, rational function in detail, including critical points and extrema



Conclusion- Sketch a general polynomial and rational function with asymptotes and extrema



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Inflection Points and Curve Sketching




- demonstrate an understanding of the concept of inflections points- demonstrate an understanding of the concept of the rate for rate of change- demonstrate the ability to sketch a function in general




ACCOMODATIONS:



Introduction- Showing the general curve sketching procedures and the key points



Conclusion- Sketching any given function with inflection points, x,y-int, critical points, and extrema









The evaluation strategies for this lesson will include:- Summative evaluation for Unit 3 – Exponential and Curve Sketching








Conclusion- Summative Evaluation for the third unit



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Introduction to Vectors




- demonstrate an understanding of the concept of scalars and vectors- demonstrate an understanding of magnitude and direction, and various forms and representations of

vectors, including quadrant bearing, true bearing, etc- demonstrate an understanding of the concept of scalar multiplication- demonstrate an understanding of the concept of vector additions graphically




ACCOMODATIONS:



Introduction- Introduction to vector as a representation of a combination of magnitude and direction



Conclusion- Show vector addition graphically and able to interpret its meaning to a relevant application



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Manipulations of Vectors




- demonstrate an understanding of the concept various algebraic manipulations in vectors- demonstrate the ability to add/subtract simple vectors in one dimension- demonstrate the ability to break vectors in 2D into its components




ACCOMODATIONS:



Introduction- Techniques in algebra to manipulate vectors (add, subtract, scalar multiplication) and breaking vectors into its components



Conclusion- Breaking vectors into its components and perform operations of them



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Applications using Vectors




- demonstrate an understanding of the available applications by using vector addition- demonstrate the ability to model a situation using vectors- demonstrate the ability to solve applications with vector manipulations




ACCOMODATIONS:



Introduction- Introducing modelling and problem solving techniques for applications involving vectors



Conclusion- Solve various application involving vector manipulations (add, subtract, and scalar multiples)



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: The Dot Product




- demonstrate an understanding of the concept of dot product and its geometric significance- demonstrate the ability to evaluate algebraically the dot product between vectors- demonstrate the ability to solve relevant geometric or real life applications using dot products




ACCOMODATIONS:



Introduction- Introducing various techniques for evaluating and modelling an application using dot product



Conclusion- Solve problems, geometric or real life application, by using the dot product



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: The Cross Product




- demonstrate an understanding of the concept of the cross product and its geometric significance- demonstrate the ability to evaluate algebraically the dot product between vectors- demonstrate the ability to solve problems involving the cross product




ACCOMODATIONS:



Introduction- Introducing the various available applications in using the cross product



Conclusion- Solve applications, geometric or real life applications, by using the cross product



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Projection and Distance




- demonstrate an understanding the concept of projection- demonstrate an understanding the concept of distance between geometric figures graphically- demonstrate the ability to find distance between geometric figures algebraically using projections




ACCOMODATIONS:



Introduction- Deriving the equation for projections- Making the connection between projection and distance between geometric figures



Conclusion- Find distance between geometric figures by using vector projection



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Applications of Cartesian Vectors




- demonstrate an understanding of the various applications available in vectors manipulation, including physics applications related to force and work

- demonstrate the ability to model a situation using vectors- demonstrate the ability to solve applications involving vectors




ACCOMODATIONS:



Introduction- Introducing modelling and solving techniques for applications



Conclusion- Solve applications using vectors









The evaluation strategies for this lesson will include:- Summative evaluation for Unit 4 – Cartesian Vectors











LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Properties of A Line




- demonstrate an understanding of the various forms of representation of a line in 2D and 3D space- demonstrate an understanding of the various properties for a line in 2D and 3D space- demonstrate the ability to convert and verify various properties for a line in 2D and 3D space- demonstrate the ability to represent a line under various conditions in 2D and 3D space




ACCOMODATIONS:



Introduction- Demonstrate techniques in manipulating algebra regarding equations of a line in 2D and 3D



Conclusion- Convert, transform, and verify various properties from all forms of an equation of a line



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Properties of A Plane




- demonstrate an understanding of the various forms of representation of a plane in 3D space- demonstrate an understanding of the various properties for a plane in 3D space- demonstrate the ability to convert and verify various properties for a plane in 3D space




ACCOMODATIONS:



Introduction- Demonstrate techniques in manipulation of a plane in 3D space



Conclusion- Solve various problems in 3D space regarding planes with restricted conditions



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Interceptions between A Line and A Plane




- demonstrate an understanding of the geometric interactions between a line and a plane- demonstrate the ability to find the solution of the interceptions between a line and a plane algebraically




ACCOMODATIONS:



Introduction- Demonstrate techniques in manipulation algebraically to find the required condition(s) for a given interaction between a line and a plane



Conclusion- Solve various geometric and algebraic applications regarding the interceptions between a line and a plane



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Distance between Geometric Figures




- demonstrate an understanding of the geometric interactions between figures (point, line, plane)- demonstrate an understanding of the various formations graphically by providing a sketch- demonstrate the ability to solve algebraically the interception point, or interception line between or

among geometric figures




ACCOMODATIONS:



Introduction- Presenting various forms of geometric configurations between figures



Conclusion- Solve algebraically (or graphically) the problem related to geometric configurations between geometric figures (point, line, plane)



LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Interception between Planes




- demonstrate an understanding of the various geometric configurations between/among two/three planes- demonstrate an understanding of the concept of interception between/among two/three planes- demonstrate the ability to solve algebraically the interception between/among two/three planes- demonstrate the ability to use the triple scalar product to determine the collinearality of the planes, and

thus to determine whether there is a point interception of not




ACCOMODATIONS:



Introduction- Demonstrate various techniques in solving algebraically the interception between/among two/three planes



Conclusion- Solve algebraically the interception among planes in 3D space









The evaluation strategies for this lesson will include:- Summative evaluation for Unit 5 – Lines and Planes











LESSON PLANCOURSE: MCV4U UNIT/TOPIC: Final Examination



CURRICULUM EXPECTATIONS: Final review day, no new curriculum expectation is taught.


- no assessment for Day 37

The evaluation strategies for this lesson will include:- Final Examination (3 hours)

ACCOMODATIONS: The following list is the accommodations for the final examination- All students are allowed to bring to with them an A4 size aim-sheet hand written or typed

on both sides to the examination- Students who have difficulty in English are permitted to use a paper dictionary, but not an

electronic dictionary- The teacher may prompt student at question and/or provide hints to the question for

students who have an Independent Education Plan


Introduction- Final Examination

Middle- Final Examination

Conclusion- Final Examination


Follow-up/Homework/Extensions/RemindersFinal Examination

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MCV4U - Lesson Plan - GZhang